The Palestinians remain trapped in a terminal on the Egyptian side of the border after it was closed by Israel on June 25, following the capture of an Israeli soldier by Palestinian militants.
The Red Cross has proposed escorting the stranded Palestinians into Gaza by boat from el-Arish along the Egyptian coast but it has yet to receive a response from either side.
Israel, which started a military offensive in Gaza after the soldier's capture, said it has offered to let the Palestinians pass through the nearby Kerem Shalom border crossing into Gaza.
Palestinian officials have rejected the Israeli proposal, insisting that Rafah be reopened.
"Why now move things to Kerem Shalom? If we move it to Kerem Shalom, we're worried they will close Rafah for good," said Saeb Erekat, an aide to Mahmoud Abbas, the Palestinian president.
At least two stranded Palestinians have died, including a 15-year-old boy who was waiting to cross into Gaza after undergoing heart surgery in Cairo, an Egyptian official at the border said.
Bana Sayeh, a spokeswoman for the Red Cross in Jerusalem, said on Monday that a total of 578 people were now stranded inside the terminal on the Egyptian side of the crossing.
"They can't cross into Gaza or back into Egypt," Sayeh said.
Palestinians technically control the Rafah crossing but its operations are overseen by European monitors and can be blocked by the Israelis. The others are controlled by Israel.
Mark Regev, an Israeli foreign ministry spokesman, said Israel has offered to let Palestinians in need of medical care to use of Kerem Shalom and the Erez crossing.
"As far as Israel is concerned, the Israeli-controlled crossings remain open for humanitarian cases," he said.
The Red Cross said it has provided funds to the Egyptian Red Crescent, which is taking the lead in providing humanitarian supplies to those stranded at the terminal.